KNO scaling, memorylessness and maximal entanglement at universal fixed point

Abstract: We analyze the experimental data of $\mathtt{p}\mathtt{-}\mathtt{p}$ collisions by the ATLAS and confront it with the AGK model developed by two of the authors, the Kharzeev-Levin~(KL) model and the simple exponential behavior for the Koba, Nielsen and Olesen~(KNO) scaling function. We show that all three models virtually coincide with all available experimental curves crossed at value $z=n/\langle n \rangle$ of the KNO scaling parameter in the broad range of the center-of-mass energies. The theoretical results and the experimental data show that the KNO violating terms are highly suppressed in the vicinity of $z=2$. The special status of the universal scaling point $z=2$, where the KNO scaling is restored for $\mathtt{p}\mathtt{-}\mathtt{p}$ collisions, suggests that it originates from statistical saturation of the optical theorem. We claim that any unitary model that approximates memoryless distribution in the high energy limit must have the same KNO scaling function $e^{-z}$ in the vicinity of $z=2$ with KNO violating corrections of the order of one over average multiplicity squared. This reflects the maximal entanglement of the final states.